If-A-M-n-n-A-2-A-1-k-R-Find-I-kA-1-

Question Number 199001 by mnjuly1970 last updated on 26/Oct/23

I f, A \in M_{n \times n}, A^{2} = A, 1 \neq k \in R .

F i n d {(I - k A)}^{- 1} = ?

Answered by MM42 last updated on 26/Oct/23

i f ∣ A ∣\neq 0

\Rightarrow A^{2} = A \overset{\times A^{- 1}}{\Rightarrow} A = I

\Rightarrow {(I - k A)}^{- 1} = {(I - k I)}^{- 1} = \frac{1}{1 - k} I ✓

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